No, you paid for your unemployment compensation while you where working or rather your employer did. You do not have to pay it back and it will have no adverse affect on your credit history or when you apply for any positions in the future.
As long as you were actually "laid-off", you will not have to pay back the unemployment, it will not affect your credit score or hinder your prospects with future employers. You typically only have to pay back unemployment if you obtain it fraudulently; i.e. you say you were "laid-off", when you were really terminated for misconduct of some sort.